Mixture density separation as a tool for high-quality interpretation of multi-source remote sensing data and related issues

The end user often needs to define extremely complex interpretation tasks and to require the analysis results to be quantitatively proven for each pixel without the test data. To this end, this paper extends the ideas underlying the modelbased unsupervised classification method previously proposed by us (Koltunov and Ben-Dor 2001). Consistently with that method, the quality of assigning a pixel to a cluster is defined as the lower confidence bound (l.c.b.) of the corresponding posterior probability estimate. We propose to compute the l.c.b.s in an approximate way using the Fisher information matrix instead of the bootstrap scheme suggested previously, leading to an l.c.b.-estimation procedure that is faster by a factor of hundreds to thousands, while being reasonably accurate. The issue of selecting the number of clusters is considered in accordance with the quantitative requirements for the level of detail and the reliability of the thematic interpretation. Specifically, the l.c.b.s form a novel selection criterion that allows the most detailed landscape descriptions to be provided with at least a pre-specified value of confidence. This implies detection of highly overlapping clusters, leading to very detailed segmentations. Consequently, numerous thematic classification and object detection problems can be solved, based on single clustering and assuming that thematic classes are unions of components. Then the thematic classification accuracy can be computed in a well-founded manner for each separate pixel, using the obtained covariance matrices of the posterior probability estimators of component membership. The procedures for thematic mapping and object detection are described. The accuracy of the l.c.b. estimation and stability of the new criterion in choosing the number of clusters are illustrated on simulated datasets. The hyperspectral data analysis experiment performed demonstrates part of the developments described in this paper. Several issues that are relevant for remote sensing data interpretation are addressed constructively. In particular, we draft the novel algorithms that use model-based cluster analysis for detection and recognition of remotely sensed objects based on prior information on their size and shape. In addition, we introduce a generalized approach to unsupervised feature extraction from data acquired by a plurality of sensors of different physical nature. A new data model generalizing the traditional Gaussian mixture model is also presented.